The disappearing icon is a known bug for iOS 10 (and was resolved in 10.3.3). If this is happening, please ensure you are running the latest version. 

However, if you are unable to update your firmware, you can follow the below instructions to see what your WIFI/LTE icons are doing...

1. While on WIFI at home, without VPN launched, make sure you are seeing the WIFI icon on the iPhone and go to some site - ensure it's working. Assuming everything is fine, go to step 2. 

2. Now go back to the main Settings screen 

3. You should see a VPN toggle option 5th or 6th place down 

4. Toggle VPN on manually - it should connect normally after 1 - 3 seconds. When it does, look at the icons - you should see the WIFI icon and then the VPN icon - as it should 

5. Navigate to a website and see that it is still working 

6. This will verify that your Private Internet Access service is working as expected. 

7. Go back to the beginning and re-enable on-demand to on 

8. If you have the bug, what you will see is suddenly and mysteriously, your WIFI icon will disappear while the VPN is connecting and may or may not be replaced with the LTE icon 

9. So after a few seconds - or a bit longer both the WIFI and VPN icons appear together like everything was normal. 

10. So the buggy process is as follows while on WIFI with on-demand ON: VPN Starts>WIFI icon disappears>nothing seems to happen for a few seconds>then both WIFI and VPN appear together 

This is a bug introduced by Apple with 10 as they added networking features and enhancements and it's been frustrating for VPN users all over the world.